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Introduction and Results

  • Eli Levin
  • Doron S. Lubinsky
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

Let I be a finite or infinite interval and let w: I → [0, ∞) be measurable with all power moments
$$ \int_{I} {{x^{n}}w(x)dx,{\text{ n = 0, 1, 2, 3,}}...} "$$
finite. Then we call w a weight and may define orthonormal polynomials
$$ {p_{n}}(x) = {p_{n}}(w,{\text{ }}x) = {\gamma _{n}}(w){x^{n}} + \cdot \cdot \cdot ,{\gamma _{n}}(w) > 0, "$$
satisfying
$$ \int_{I} {{p_{n}}{p_{m}}w = {d_{{mn}}},m, n = 0, 1, 2,... .} "$$

Keywords

Orthogonal Polynomial Polynomial Growth Infinite Interval Markov Inequality Orthonormal Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Eli Levin
    • 1
  • Doron S. Lubinsky
    • 2
  1. 1.Department of MathematicsThe Open University of IsraelTel AvivIsrael
  2. 2.Centre for Applicable Analysis and Number Theory Department of MathematicsWitwatersrand UniversityWitsSouth Africa

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